Mangogirl,
The JTB and the Ministry of Tourism are fully aware of the issue. They are seeking the best solution, looking at all options from formal regulations and licensing to out right banning.
Since it is so popular with the visitors to Jamaica, I personally feel that the regulatory and licensing option will end up being the one chosen.
It is the old game of supply and the demand. If there was no demand for the horses, there would be no supply...